Finite Group Databasebeta

← #11866191

Subgroups — #11866191

Order 1152.

1122 conjugacy classes of subgroups.

The subgroup lattice has 909 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5545C211yesmaximal, characteristic, complemented
2C2×#63934C211yesmaximal, characteristic, complemented
3C2×D3×#213C211yesmaximal, characteristic, complemented
4#10594001C211yesmaximal, characteristic, complemented
5#10592714C211yesmaximal, characteristic, complemented
6C3×#5016C211yesmaximal, characteristic, complemented
7#10591481C211yesmaximal, characteristic, complemented
8#10591471C211yesmaximal, characteristic, complemented
9#10590610C211yesmaximal, characteristic, complemented
10#10590592C211yesmaximal, characteristic, complemented
11#10590547C211yesmaximal, characteristic, complemented
12#10590534C211yesmaximal, characteristic, complemented
13#10590349C211yesmaximal, characteristic, complemented
14#10590348C211yesmaximal, characteristic, complemented
15#10590324C211yesmaximal, characteristic, complemented
16#82540—31nomaximal
17#80536—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20C2×#3799C2211yescharacteristic
21C32×C4×D4C2211yescharacteristic, complemented
22C2×#3753C2211yescharacteristic
23C2×#3753C2211yescharacteristic, complemented
24#64083C2211yescharacteristic, complemented
25C3×D4×Dic3C2211yescharacteristic, complemented
26C2×C3×#214C2211yescharacteristic, complemented
27C2×C3×#213C2211yescharacteristic
28C3×C4×#67—21no—
29C2×C3×(C2×D3)⋊C4—21no—
30C3×#893C2211yescharacteristic, complemented
31C3×#892C2211yescharacteristic
32C3×#67⋊C4—21no—
33C3×D3×C22⋊C4—21no—
34C3×#875C2211yescharacteristic, complemented
35C3×C4×D12C2211yescharacteristic, complemented
36C3×#872C2211yescharacteristic
37#63934—24no—
38D3×#213—24no—
39#63923—21no—
40#63923—21no—
41#63911C2211yescharacteristic, complemented
42#63910—21no—
43#63910—21no—
44#63864C2211yescharacteristic, complemented
45C2×#3715C2211yescharacteristic, complemented
46C2×#3714C2211yescharacteristic
47C2×#3714C2211yescharacteristic, complemented
48C2×#3713C2211yescharacteristic
49C2×#3711C2211yescharacteristic
50C2×D3×C3⋊C8C2211yescharacteristic
51#63636C2211yescharacteristic, complemented
52#63636C2211yescharacteristic, complemented
53C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
54C3×#810C2211yescharacteristic, complemented
55C3×#809C2211yescharacteristic, complemented
56C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
57Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
58Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63565C2211yescharacteristic, complemented
60#63564C2211yescharacteristic, complemented
61#63564C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63C3×#518—31no—
64C2×#932—31no—
65C22×#213—31no—
66C2×#914—31no—
67C2×D3×D8—31no—
68#5674—31no—
69#5545D311yescharacteristic, complemented
70#5525—31no—
71C3×#463—31no—
72#5165—31no—
73#5150—31no—
74#5057—31no—
75#5016—31no—
76#5016—31no—
77#5016—31no—
78#5016D311yescharacteristic, complemented
79#5015—31no—
80#5015—31no—
81#5015—31no—
82#5015—31no—
83#5015—31no—
84#5015—61no—
85#5002—31no—
86#5001—31no—
87#4999—31no—
88#4843—31no—
89#4839—31no—
90#4819—31no—
91#4804—31no—
92#4786—31no—
93#4770—31no—
94C23×C3×D3—21no—
95C22×D32—21no—
96C2×C32×D4C2311yescharacteristic
97C22×C32×C4—21no—
98C2×C4⋊(C3⋊D3)—21no—
99C2×C4⋊(C3⋊D3)—21no—
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C4⋊(C3⋊D3)C2311yescharacteristic
102C2×C3×#67—21no—
103C22×C3×Dic3—21no—
104C3×D3×D4—22no—
105C3×D3×D4D414yescomplemented
106C2×C3×D12C2311yescharacteristic
107C2×C3×D12C2311yescharacteristic
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3—21no—
110C2×C3×C4×D3C2311yescharacteristic
111C2×C3×Dic6C2311yescharacteristic
112C2×#626—21no—
113C2×#626—21no—
114C2×#626—21no—
115C2×#626—21no—
116C2×#624—21no—
117D3×D12—22no—
118D3×D12—22no—
119#3799—22no—
120#3799—22no—
121C32×C4⋊C4C2311yescharacteristic
122C32×C22⋊C4—21no—
123C32×C42C2311yescharacteristic
124#3753—22no—
125#3753—22no—
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127C2×C3⋊(C3⋊C8)C2311yescharacteristic
128C3×#217—21no—
129C3×#214—22no—
130C3×#213—22no—
131C3×(C2×D3)⋊C4—21no—
132C3×(C2×D3)⋊C4—21no—
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4D411yescharacteristic
137C3×(C2×D3)⋊C4D411yescharacteristic
138C3×C4⋊Dic3C2311yescharacteristic
139C3×Dic3⋊C4D411yescharacteristic
140C3×Dic3⋊C4D411yescharacteristic
141C3×C4×Dic3—21no—
142C3×C4×Dic3C2311yescharacteristic
143C2×C3×C3⋊C8C2311yescharacteristic
144C2×C3×C3⋊C8C2311yescharacteristic
145#3722—21no—
146#3722—21no—
147#3715—22no—
148#3714—22no—
149#3714—22no—
150#3713—22no—
151#3711—22no—
152D3×C3⋊C8—22no—
153#3041—91noSylow
154C22×C3×D4—31no—
155C2×#239—31no—
156C2×D3×D4—31no—
157C2×D3×D4C2×D311yescharacteristic
158C2×#235—31no—
159C22×D12—31no—
160C2×C3×SD16—31no—
161C2×C3×D8—31no—
162C3×#124—31no—
163C3×C4×D4—21no—
164C3×C4×D4—31no—
165C3×C4×D4—31no—
166C3×C4×D4—31no—
167C3×C4×D4—61no—
168C3×C4×D4—61no—
169C3×C4×D4C2×D311yescharacteristic, complemented
170C3×C4×D4C2×D311yescharacteristic, complemented
171C3×#117—31no—
172C3×#117—31no—
173C2×C3×C22⋊C4—61no—
174C2×C3×C22⋊C4—61no—
175#947—31no—
176C2×#215—31no—
177#940—31no—
178D4×Dic3C2×D311yescharacteristic, complemented
179C2×#214—31no—
180C2×#214C2×D311yescharacteristic, complemented
181#932—64no—
182C2×#213—31no—
183C2×#213—31no—
184C2×#213—31no—
185C2×#213—31no—
186C2×#213—31no—
187C2×#213—31no—
188C2×#213—31no—
189C2×#213—31no—
190C2×#213—61no—
191C2×#213—61no—
192C2×#213—64no—
193C2×#213C2×D311yescharacteristic
194C4×#67—21no—
195C2×(C2×D3)⋊C4—21no—
196C2×#208—31no—
197C22×C3⋊C8—31no—
198#914—64no—
199D3×D8—64no—
200C2×D24—31no—
201C2×D24—31no—
202C2×ΓL(1,𝔽25)—31no—
203C2×D3×C8—31no—
204#895—61no—
205#895—61no—
206#893C2×D311yescharacteristic, complemented
207#892C2×D311yescharacteristic
208#884—61no—
209#884—61no—
210#882—61no—
211#882—61no—
212#882—61no—
213#882—61no—
214#67⋊C4—21no—
215D3×C22⋊C4—21no—
216#875—31no—
217#875C2×D311yescharacteristic, complemented
218#874—31no—
219#874—31no—
220#874—31no—
221#874—61no—
222C4×D12C2×D311yescharacteristic, complemented
223#872C2×D311yescharacteristic
224C3×C4⋊C8—31no—
225C3×#103—31no—
226C3×#102—31no—
227#835—31no—
228#832—31no—
229#821—31no—
230#821—31no—
231Dic3⋊C8—31no—
232Dic3⋊C8—31no—
233#810—31no—
234#810C2×D311yescharacteristic, complemented
235#809—31no—
236#809—31no—
237#809—31no—
238#809—31no—
239#809—31no—
240#809—31no—
241#809—31no—
242#809—61no—
243#809—61no—
244#809C2×D311yescharacteristic, complemented
245C4⋊(C3⋊C8)—31no—
246C4⋊(C3⋊C8)—31no—
247C4⋊(C3⋊C8)—31no—
248C4⋊(C3⋊C8)—31no—
249C4⋊(C3⋊C8)—61no—
250C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
251C23×C32—21no—
252C22×C3⋊D3—21no—
253C22×C3⋊D3—21no—
254C22×C3×D3—21no—
255C22×C3×D3—24no—
256C22×C3×D3—21no—
257C22×C3×D3—81no—
258C22×C3×D3—81no—
259C22×C3×D3C2×D411yescharacteristic
260C2×D32—42no—
261C2×D32—81no—
262C2×D32—81no—
263C32×D4—21no—
264C32×D4C2×D412yes—
265C2×C32×C4—21no—
266C2×C32×C4—81no—
267C2×C32×C4C2×D411yescharacteristic
268C2×C32×C4C2×D411yescharacteristic
269C2×C32×C4C2411yescharacteristic
270C4⋊(C3⋊D3)—21no—
271C4⋊(C3⋊D3)—21no—
272C4⋊(C3⋊D3)—21no—
273C4⋊(C3⋊D3)—21no—
274C4⋊(C3⋊D3)—81no—
275C4⋊(C3⋊D3)—81no—
276C3×#67—24no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—81no—
280C2×C3×Dic3C2×D411yescharacteristic
281C2×C3×Dic3C2×D411yescharacteristic
282C2×C3×Dic3C2×D411yescharacteristic
283C3×D12—21no—
284C3×D12—21no—
285C3×D12—21no—
286C3×D12C2×D412yes—
287C3×C4×D3—81no—
288C3×C4×D3—81no—
289C3×C4×D3C2×D412yes—
290C3×C4×D3#4112yes—
291C3×Dic6—21no—
292C3×Dic6—21no—
293#626—42no—
294#626—42no—
295#626—81no—
296#626—81no—
297#624—42no—
298C3⋊(C3⋊C8)—21no—
299C3⋊(C3⋊C8)—21no—
300C3×C3⋊C8—21no—
301C3×C3⋊C8—21no—
302C2×AGL(1,ℤ/8)—91no—
303C22×D8—91no—
304#535—91no—
305#518—31no—
306#463—31no—
307#463—91no—
308#463—91no—
309#463—91no—
310#459—91no—
311#459—91no—
312#459—91no—
313#459—91no—
314#424—91no—
315#418—91no—
316#416—91no—
317C24×C3—61no—
318C23×D3—21no—
319C23×D3—61no—
320C23×D3—61no—
321C2×C3×Q8—31no—
322C2×C3×D4—21no—
323C2×C3×D4—34no—
324C2×C3×D4—31no—
325C2×C3×D4—31no—
326C2×C3×D4—62no—
327C2×C3×D4—61no—
328C2×C3×D4C22×D311yescharacteristic
329C2×C3×D4C22×D311yescharacteristic
330C22×C3×C4—21no—
331C22×C3×C4—21no—
332C22×C3×C4—31no—
333C22×C3×C4—41no—
334C22×C3×C4—61no—
335C22×C3×C4—61no—
336C22×C3×C4—61no—
337C2×#67—21no—
338C2×#67—61no—
339C2×#67—61no—
340C2×#67—61no—
341C2×#67—61no—
342C22×Dic3—21no—
343#239—62no—
344#239—62no—
345D3×D4—22no—
346D3×D4—62no—
347D3×D4—62no—
348D3×D4D1214yescomplemented
349#235—62no—
350#235—62no—
351C2×D12—31no—
352C2×D12—31no—
353C2×D12—31no—
354C2×D12—31no—
355C2×D12—61no—
356C2×D12—61no—
357C2×D12—62no—
358C2×D12—62no—
359C2×D12—61no—
360C2×D12—61no—
361C2×D12—61no—
362C2×D12—61no—
363C2×D12—61no—
364C2×D12—61no—
365C2×D12—61no—
366C2×D12—61no—
367C2×D12—121no—
368C2×D12—121no—
369C2×D12C22×D311yescharacteristic
370C2×D12C22×D311yescharacteristic
371C2×C4×D3—21no—
372C2×C4×D3—21no—
373C2×C4×D3—61no—
374C2×C4×D3—61no—
375C2×C4×D3C22×D311yescharacteristic
376C2×Dic6C22×D311yescharacteristic
377C3×SD16—62no—
378C3×D8—62no—
379C2×C3×C8—31no—
380C2×C3×C8—31no—
381C3×C4⋊C4—21no—
382C3×C4⋊C4—31no—
383C3×C4⋊C4—31no—
384C3×C4⋊C4—31no—
385C3×C4⋊C4C22×D311yescharacteristic
386C3×C4⋊C4C22×D311yescharacteristic
387C3×C22⋊C4—21no—
388C3×C22⋊C4—21no—
389C3×C22⋊C4—31no—
390C3×C22⋊C4—31no—
391C3×C22⋊C4—41no—
392C3×C22⋊C4—61no—
393C3×C22⋊C4—61no—
394C3×C22⋊C4—61no—
395C3×C22⋊C4—61no—
396C3×C22⋊C4—61no—
397C3×C22⋊C4—61no—
398C3×C42—21no—
399C3×C42—31no—
400C3×C42—61no—
401C3×C42C22×D311yescharacteristic
402C3×C42C22×D311yescharacteristic
403#217—21no—
404#215—62no—
405#214—22no—
406#214—62no—
407#213—22no—
408#213—62no—
409#213—62no—
410#213—62no—
411#213—62no—
412#213—62no—
413#213—62no—
414#213—62no—
415#213—62no—
416#213—122no—
417#213—122no—
418(C2×D3)⋊C4—21no—
419(C2×D3)⋊C4—21no—
420(C2×D3)⋊C4—21no—
421(C2×D3)⋊C4—21no—
422(C2×D3)⋊C4—21no—
423(C2×D3)⋊C4—61no—
424(C2×D3)⋊C4—61no—
425(C2×D3)⋊C4—61no—
426(C2×D3)⋊C4—61no—
427(C2×D3)⋊C4#6711yescharacteristic
428(C2×D3)⋊C4#6711yescharacteristic
429C4⋊Dic3C22×D311yescharacteristic
430Dic3⋊C4#6711yescharacteristic
431Dic3⋊C4#6711yescharacteristic
432C4×Dic3—21no—
433C4×Dic3C22×D311yescharacteristic
434#208—62no—
435C2×C3⋊C8—31no—
436C2×C3⋊C8—31no—
437C2×C3⋊C8—31no—
438C2×C3⋊C8—31no—
439C2×C3⋊C8—61no—
440C2×C3⋊C8—61no—
441C2×C3⋊C8—62no—
442C2×C3⋊C8C22×D311yescharacteristic
443C2×C3⋊C8C22×D311yescharacteristic
444D24—62no—
445D24—62no—
446ΓL(1,𝔽25)—62no—
447D3×C8—62no—
448C22×C32—22no—
449C22×C32—41no—
450C22×C32—41no—
451C22×C32C22×D411yescharacteristic
452C2×C3⋊D3—41no—
453C2×C3⋊D3—41no—
454C2×C3⋊D3—41no—
455C2×C3⋊D3—41no—
456C2×C3⋊D3—41no—
457C2×C3⋊D3—41no—
458C2×C3×D3—21no—
459C2×C3×D3—21no—
460C2×C3×D3—22no—
461C2×C3×D3—41no—
462C2×C3×D3—41no—
463C2×C3×D3—41no—
464C2×C3×D3—41no—
465C2×C3×D3—41no—
466C2×C3×D3—84no—
467C2×C3×D3#12112yes—
468D32—84no—
469C32×C4—21no—
470C32×C4—21no—
471C32×C4—41no—
472C32×C4C22×D411yescharacteristic
473C32×C4C2×#4111yescharacteristic
474C3×Dic3—21no—
475C3×Dic3—21no—
476C3×Dic3—41no—
477C3×Dic3—41no—
478C3×Dic3#12112yes—
479C2×#41—91no—
480C22×D4—31no—
481C22×D4—91no—
482AGL(1,ℤ/8)—184no—
483C2×SD16—31no—
484C2×SD16—91no—
485C2×D8—31no—
486C2×D8—91no—
487C2×D8—91no—
488C2×D8—91no—
489C2×D8—91no—
490C2×D8—91no—
491C2×D8—184no—
492C2×M16—91no—
493C22×C8—91no—
494#127—91no—
495#127—91no—
496#124—31no—
497#124—91no—
498#121—181no—
499#121—181no—
500#120—181no—
501#120—181no—
502C4×D4—31no—
503C4×D4—31no—
504C4×D4—31no—
505C4×D4—61no—
506C4×D4—61no—
507C4×D4D3211yescharacteristic, complemented
508#117—31no—
509#117—31no—
510C2×C22⋊C4—61no—
511C2×C22⋊C4—61no—
512C4⋊C8—31no—
513C4⋊C8—91no—
514C4⋊C8—91no—
515C4⋊C8—91no—
516#103—31no—
517#103—91no—
518#102—31no—
519#102—91no—
520#102—91no—
521#102—91no—
522#102—91no—
523#102—91no—
524C23×C3—21no—
525C23×C3—21no—
526C23×C3—31no—
527C23×C3—41no—
528C23×C3—64no—
529C23×C3—61no—
530C23×C3—61no—
531C23×C3—241no—
532C23×C3—241no—
533C22×D3—21no—
534C22×D3—24no—
535C22×D3—21no—
536C22×D3—61no—
537C22×D3—61no—
538C22×D3—61no—
539C22×D3—61no—
540C22×D3—81no—
541C22×D3—81no—
542C22×D3—121no—
543C22×D3—121no—
544C22×D3—122no—
545C22×D3—122no—
546C22×D3—241no—
547C22×D3—241no—
548C22×D3—241no—
549C22×D3—241no—
550C22×D3C2×#6711yescharacteristic
551C3×Q8—61no—
552C3×Q8—61no—
553C3×D4—21no—
554C3×D4—21no—
555C3×D4—22no—
556C3×D4—32no—
557C3×D4—41no—
558C3×D4—64no—
559C3×D4—61no—
560C3×D4—61no—
561C3×D4—61no—
562C3×D4C2×D1212yes—
563C3×D4D3×D412yes—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—31no—
570C2×C3×C4—32no—
571C2×C3×C4—32no—
572C2×C3×C4—31no—
573C2×C3×C4—31no—
574C2×C3×C4—41no—
575C2×C3×C4—61no—
576C2×C3×C4—61no—
577C2×C3×C4—81no—
578C2×C3×C4—81no—
579C2×C3×C4—82no—
580C2×C3×C4—241no—
581C2×C3×C4—241no—
582C2×C3×C4—241no—
583C2×C3×C4D3×D411yescharacteristic
584C2×C3×C4D3×D411yescharacteristic
585C2×C3×C4C2×#6711yescharacteristic
586C2×C3×C4C2×#6711yescharacteristic
587C2×C3×C4C23×D311yescharacteristic
588C2×C3×C4C23×D311yescharacteristic
589#67—24no—
590#67—122no—
591#67—122no—
592#67—241no—
593#67—241no—
594C2×Dic3—21no—
595C2×Dic3—21no—
596C2×Dic3—81no—
597C2×Dic3C2×#6711yescharacteristic
598C2×Dic3C2×#6711yescharacteristic
599C2×Dic3C2×#6711yescharacteristic
600D12—21no—
601D12—21no—
602D12—21no—
603D12—61no—
604D12—61no—
605D12—61no—
606D12—61no—
607D12—61no—
608D12—61no—
609D12—61no—
610D12—61no—
611D12—121no—
612D12—121no—
613D12—121no—
614D12—121no—
615D12—122no—
616D12—122no—
617D12—241no—
618D12—241no—
619D12—241no—
620D12—241no—
621D12—242no—
622D12—242no—
623D12—241no—
624D12—241no—
625D12C2×D1212yes—
626C4×D3—81no—
627C4×D3—81no—
628C4×D3—122no—
629C4×D3—122no—
630C4×D3C2×D1212yes—
631C4×D3#23512yes—
632Dic6—21no—
633Dic6—21no—
634C3×C8—61no—
635C3×C8—61no—
636C3⋊C8—21no—
637C3⋊C8—21no—
638C3⋊C8—61no—
639C3⋊C8—61no—
640C3⋊C8—61no—
641C3⋊C8—61no—
642C3⋊C8—121no—
643C3⋊C8—121no—
644C2×C32—42no—
645C2×C32C2×#12111yescharacteristic
646C2×C32#57611yescharacteristic
647C2×C32#57611yescharacteristic
648C3⋊D3—81no—
649C3⋊D3—81no—
650C3×D3—22no—
651C3×D3—42no—
652C3×D3—81no—
653C24—61no—
654C24—181no—
655#41—182no—
656#41—182no—
657C2×Q8—31no—
658C2×D4—34no—
659C2×D4—31no—
660C2×D4—31no—
661C2×D4—62no—
662C2×D4—61no—
663C2×D4—91no—
664C2×D4—91no—
665C2×D4—182no—
666C2×D4—182no—
667C2×D4—181no—
668C2×D4—181no—
669C2×D4—181no—
670C2×D4—181no—
671C2×D4—181no—
672C2×D4—181no—
673C2×D4C2×D3211yescharacteristic
674C22×C4—21no—
675C22×C4—31no—
676C22×C4—61no—
677C22×C4—61no—
678C22×C4—61no—
679C22×C4—181no—
680SD16—62no—
681SD16—182no—
682D8—62no—
683D8—182no—
684D8—182no—
685D8—182no—
686D8—182no—
687D8—182no—
688M16—182no—
689C2×C8—31no—
690C2×C8—31no—
691C2×C8—91no—
692C2×C8—91no—
693C2×C8—182no—
694C4⋊C4—31no—
695C4⋊C4—31no—
696C4⋊C4—31no—
697C4⋊C4C2×D3211yescharacteristic
698C22⋊C4—21no—
699C22⋊C4—31no—
700C22⋊C4—31no—
701C22⋊C4—61no—
702C22⋊C4—61no—
703C22⋊C4—61no—
704C22⋊C4—61no—
705C22⋊C4—61no—
706C22⋊C4—61no—
707C22⋊C4—181no—
708C22⋊C4—181no—
709C42—31no—
710C42—61no—
711C42C2×D3211yescharacteristic
712C22×C3—22no—
713C22×C3—22no—
714C22×C3—21no—
715C22×C3—32no—
716C22×C3—42no—
717C22×C3—41no—
718C22×C3—41no—
719C22×C3—41no—
720C22×C3—41no—
721C22×C3—61no—
722C22×C3—61no—
723C22×C3—62no—
724C22×C3—81no—
725C22×C3—81no—
726C22×C3—121no—
727C22×C3—121no—
728C22×C3—121no—
729C22×C3—121no—
730C22×C3—121no—
731C22×C3—244no—
732C22×C3C2×D3×D411yescharacteristic
733C22×C3C22×#6711yescharacteristic
734C2×D3—21no—
735C2×D3—21no—
736C2×D3—22no—
737C2×D3—41no—
738C2×D3—41no—
739C2×D3—41no—
740C2×D3—41no—
741C2×D3—41no—
742C2×D3—84no—
743C2×D3—121no—
744C2×D3—121no—
745C2×D3—121no—
746C2×D3—121no—
747C2×D3—121no—
748C2×D3—121no—
749C2×D3—121no—
750C2×D3—121no—
751C2×D3—121no—
752C2×D3—121no—
753C2×D3—121no—
754C2×D3—121no—
755C2×D3—241no—
756C2×D3—241no—
757C2×D3—241no—
758C2×D3—241no—
759C2×D3—241no—
760C2×D3—241no—
761C2×D3—244no—
762C2×D3—244no—
763C2×D3#93012yes—
764C3×C4—22no—
765C3×C4—21no—
766C3×C4—21no—
767C3×C4—21no—
768C3×C4—21no—
769C3×C4—21no—
770C3×C4—21no—
771C3×C4—32no—
772C3×C4—41no—
773C3×C4—41no—
774C3×C4—41no—
775C3×C4—61no—
776C3×C4—61no—
777C3×C4—81no—
778C3×C4—121no—
779C3×C4—121no—
780C3×C4C22×D1211yescharacteristic
781C3×C4C2×#23511yescharacteristic
782C3×C4C2×D3×D411yescharacteristic
783C3×C4D3×#4111yescharacteristic
784Dic3—21no—
785Dic3—21no—
786Dic3—41no—
787Dic3—41no—
788Dic3#93012yes—
789C32#304111yescharacteristic, complemented, Sylow
790C23—21no—
791C23—31no—
792C23—64no—
793C23—61no—
794C23—61no—
795C23—181no—
796C23—181no—
797C23—241no—
798C23—241no—
799C23—362no—
800C23—721no—
801C23—721no—
802Q8—61no—
803Q8—61no—
804D4—21no—
805D4—32no—
806D4—64no—
807D4—61no—
808D4—61no—
809D4—61no—
810D4—181no—
811D4—181no—
812D4—181no—
813D4—181no—
814D4—362no—
815D4—362no—
816D4—721no—
817D4—721no—
818D4—721no—
819D4—721no—
820D4D3×D1212yes—
821C2×C4—21no—
822C2×C4—31no—
823C2×C4—32no—
824C2×C4—32no—
825C2×C4—31no—
826C2×C4—31no—
827C2×C4—61no—
828C2×C4—61no—
829C2×C4—81no—
830C2×C4—241no—
831C2×C4—241no—
832C2×C4—241no—
833C2×C4—362no—
834C2×C4D3×#6711yescharacteristic
835C2×C4D3×#6711yescharacteristic
836C2×C4C22×D3211yescharacteristic
837C8—61no—
838C8—61no—
839C8—181no—
840C8—181no—
841C2×C3—21no—
842C2×C3—21no—
843C2×C3—21no—
844C2×C3—42no—
845C2×C3—42no—
846C2×C3—62no—
847C2×C3—82no—
848C2×C3—122no—
849C2×C3—241no—
850C2×C3D3×#12111yescharacteristic
851C2×C3#576911yescharacteristic
852C2×C3#577411yescharacteristic
853C2×C3C2×#93011yescharacteristic
854C2×C3#583511yescharacteristic
855C2×C3#583511yescharacteristic
856D3—22no—
857D3—42no—
858D3—81no—
859D3—241no—
860D3—241no—
861D3—241no—
862D3—241no—
863D3—481no—
864D3—481no—
865C22—22no—
866C22—32no—
867C22—41no—
868C22—41no—
869C22—61no—
870C22—61no—
871C22—62no—
872C22—121no—
873C22—121no—
874C22—121no—
875C22—121no—
876C22—121no—
877C22—244no—
878C22—361no—
879C22—361no—
880C22—361no—
881C22—361no—
882C22—361no—
883C22—361no—
884C22—724no—
885C22C2×D3×#6711yescharacteristic
886C4—21no—
887C4—21no—
888C4—32no—
889C4—41no—
890C4—61no—
891C4—61no—
892C4—121no—
893C4—121no—
894C4C2×D3×D1211yescharacteristic
895C4D3×#23511yescharacteristic
896C3—21no—
897C3#8053611yescharacteristic, complemented
898C3#8254011yescharacteristic, complemented
899C2—42no—
900C2—62no—
901C2—122no—
902C2—241no—
903C2—721no—
904C2—721no—
905C2D3×#93011yescharacteristic
906C2#1059509711yescharacteristic
907C2#1059545611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
hypercenterC4×D4D32
hypocenterC32#3041
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C3×#5545C2semidirect
2. C2×#63934C2semidirect
3. C2×D3×#213C2semidirect
4. #10594001C2semidirect
5. #10592714C2semidirect
6. C3×#5016C2semidirect
7. #10591481C2semidirect
8. #10591471C2semidirect
9. #10590610C2semidirect
10. #10590592C2semidirect
11. #10590547C2semidirect
12. #10590534C2semidirect
13. #10590349C2semidirect
14. #10590348C2semidirect
15. #10590324C2semidirect
21. C32×C4×D4C22semidirect
23. C2×#3753C22semidirect
24. #64083C22semidirect
25. C3×D4×Dic3C22semidirect
26. C2×C3×#214C22semidirect
30. C3×#893C22semidirect
34. C3×#875C22semidirect
35. C3×C4×D12C22semidirect
41. #63911C22semidirect
44. #63864C22semidirect
45. C2×#3715C22semidirect
47. C2×#3714C22semidirect
51. #63636C22semidirect
52. #63636C22semidirect
53. C4⋊(C3⋊(C3⋊C8))C22semidirect
54. C3×#810C22semidirect
55. C3×#809C22semidirect
56. C3×C4⋊(C3⋊C8)C22semidirect
57. Dic3⋊(C3⋊C8)C22semidirect
58. Dic3⋊(C3⋊C8)C22semidirect
59. #63565C22semidirect
60. #63564C22semidirect
61. #63564C22semidirect
62. #63562C22semidirect
69. #5545D3semidirect
78. #5016D3semidirect
105. C3×D3×D4D4semidirect
169. C3×C4×D4C2×D3semidirect
170. C3×C4×D4C2×D3semidirect
178. D4×Dic3C2×D3semidirect
180. C2×#214C2×D3semidirect
206. #893C2×D3semidirect
217. #875C2×D3semidirect
222. C4×D12C2×D3semidirect
234. #810C2×D3semidirect
244. #809C2×D3semidirect
250. C4⋊(C3⋊C8)C2×D3semidirect
348. D3×D4D12semidirect
507. C4×D4D32semidirect
789. C32#3041semidirect
897. C3#80536semidirect
898. C3#82540semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C3×#55452
C2×#639342
C2×D3×#2132
#105940012
#105927142
C3×#50162
#105914812
#105914712
#105906102
#105905922
#105905472
#105905342
#105903492
#105903482
#105903242
#825403
#805363